Observation of optical de Broglie–Mackinnon wave packets

Abstract

de Broglie wave packets accompanying moving particles are dispersive and lack an intrinsic length scale solely dictated by the particle mass and velocity. Mackinnon proposed a localized non-dispersive wave packet constructed out of dispersive de Broglie phase waves that possess an intrinsic length scale via an inversion of the roles of particle and observer. So far, the de Broglie–Mackinnon wave packet has remained a theoretical proposal. Here we report the observation of optical de Broglie–Mackinnon wave packets using paraxial space–time-coupled pulsed laser fields in the presence of anomalous group-velocity dispersion. Crucially, the bandwidth of de Broglie–Mackinnon wave packets has an upper limit that is compatible with the wave-packet group velocity and equivalent mass. In contrast to previously observed linear-propagation-invariant wave packets whose spatio-temporal profiles at any axial plane are X-shaped, those for de Broglie–Mackinnon wave packets are uniquely O-shaped (circularly symmetric with respect to space and time). By sculpting their spatio-temporal spectral structure, we produce dispersion-free de Broglie–Mackinnon wave packets in the dispersive medium, observe their circularly symmetric spatio-temporal intensity profiles and closed-trajectory spectra, and tune the field parameters that uniquely determine the wave-packet length scale. de Broglie–Mackinnon wave packets are an extension of matter waves, but have so far remained a theoretical construct. Combining spatio-temporal light fields with anomalous dispersion has now allowed their experimental observation.